Proof step e-014dd8a0f9594ad5

basis_map A007318 → concludes about shift_x_plus_one of Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 a16c3542c3df153725c4bba9cf73b8d61cc43d268d778ac89dba558b1e1beeb5, 6,855 bytes (1,384 compressed); download JSON

Cited by

• n-416d26cbd480eee5 (one_signed_coefficients)
• n-416d26cbd480eee5 (hadamard_kernel)
• n-416d26cbd480eee5 (real_rooted)